Question

v) If x = 2+√3, then (1/x) is equal to:
(a) 1/2+√3
(b) 1\2 +√3
(c) 2-√3
(d) 2​

Answer 1

Answer:

1/x = (2 - √3)

Step-by-step explanation:

Given that x = 2 + √3

then 1/x = 1/(2 + √3)

Now, on rationalizing the equation

=> 1/x = [ 1/(2 + √3) ] × [ (2 - √3)/(2 - √3) ]

=> 1/x = (2 - √3)/[ (2 + √3)(2 - √3) ]

=> 1/x = (2 - √3)/[ (2)² - (√3)² ]

because (a + b)(a - b) = a² - b²

=> 1/x = (2 - √3)/[ 4 - 3 ]

=> 1/x = (2 - √3)/1

=> 1/x = (2 - √3)